What is eradication of the fetter of identity-view (sakkāya-diṭṭhi)?

Eradicating the lower fetter comes from prolonged experience of anatta in meditation (and the associated liberation) however the tendency to selfing is not uprooted. Nor is craving & attraction towards sensual pleasures uprooted when a strong sensual pleasure come within the field of experience. For example, the mind of a stream-enterer may find a certain food delicious & enticing; which is sensual desire. However, a stream-enterer has sufficient purity (as described in SN 13.1) so to not crave any sensual pleasure to a degree that hinders meditation. Or a stream-enterer may not be interested in sex however the sight of an exceptionally beautiful woman may draw the mind of the stream-enterer towards the woman. This is sensual desire; even though the sensual desire does not give rise to becoming (bhava) and unwholesome thoughts towards the extremely beautiful woman. The suttas are very clear in describing arahantship as the "uprooting" of the tendencies (anusaya). A stream-enterer has not uprooted the defilements of greed, hatred & delusion however their mind has had sufficient experience of anatta do fully understand selfing is not a real self and merely a thought construct fueled by suffering. The stream-enterer has comprehended Dependent Origination as I have explained many times on this forum.

In conclusion, stream-entry did not occur in the other question because the mind did not develop confidence in the Dhamma because the mind did not clearly experience liberation from suffering with the absence of selfing. Instead, the mind experienced fear, which is not stream-entry. For stream-entry, three fetters are to be broken:

1. View of real self.

2. Doubt (vicikicchā) in Dhamma and the path

3. Superstition.

I think that a "view" is fixed: stable or permanent over time.

For example, I rarely ever think of Newton's Law of Gravitation -- but whenever I do, I imagine it to to be true (within relativistic limitations): and I will recall to mind examples of "evidence" for it (e.g. parabolic trajectories, elliptical orbits, and the fact that it's the doctrine of a space-faring culture).

If someone or something suggests that a "view" isn't true, a reaction may be to defend that view -- to reinforce or perpetuate the view, to repeat the reasoning which leads to that view.

The term is often used, e.g. in the Ditthi Sutta (AN 10.93), to refer to speculative views -- views that people have formed but which nevertheless don't have a proper (right) basis:

As for the venerable one who says, 'The cosmos is eternal. Only this is true; anything otherwise is worthless. This is the sort of view I have,' his view arises from his own inappropriate attention or in dependence on the words of another. Now this view has been brought into being, is fabricated, willed, dependently originated.

See also "thicket of views".

I think it's difficult to argue or reason with people who "hold" views -- because you might take down a house by removing its supports, but if a view has no basis to begin with then how can you approach it? -- and because people are emotionally invested (so, reason alone may not be enough).

I think that sakkāya is a doctrine or view about "the body" or the "abode of soul".

The dictionary says (with references to suttas) that it's associated with views about the five aggregates:

sakkāya
the body in being, the existing body or group (= -nikāya q.v.); as a t.t. in P. psychology almost equal to individuality; identified with the five khandhas MN.i.299; SN.iii.159; SN.iv.259; AN.ii.34; Thig.170, Thig.239; Dhs-a.348. See also DN.iii.216 (cp. Dial. Pv.iii.216#1); AN.iii.293, AN.iii.401; Mnd.109.

It's also sometimes associated with a view about contact with the senses: SN 35.167.

So, my question here is, if eradication of the lower fetter of identity-view or belief in a self (sakkāya-diṭṭhi) is not the complete eradication of a self, then what is it really?

I think it's no longer holding the view: neither for intellectual reasons, nor even for emotional reasons.

I guess that "not holding the view for emotional reasons" may require some insight into (experience and diagnosis of) dukkha associated with self-view -- i.e. a reason not to hold self-view is that the view is unsatisfactory or conducive to suffering (and anatta is seen to be compatible or not incompatible with any self-interest so there's less or no emotional resistance to it).

In other words, it's associated with seeing the three characteristics.

It's also associated with vicikicchā, as you said.

For completeness' sake, another possibility, another condition in which it may arise (i.e. an emotional willingness to consider a view in which yourself, body, isn't primary and central), is loving another as yourself -- perhaps the love experienced by a parent, or bodhicitta.

Is it an intellectual understanding of not-self? Or is it more? Is it an opinion? Is it a belief? Is it an experience?

I think it's an experience, of the three characteristics and of hearing the dhamma, and an intellectual understanding, and some (enough of an) emotional understanding.

How is the eradication of the lower fetter of identity view different from total eradication of the sense of self?

That was a topic of How are 'conceit' and 'identity-view' not the same?

In summary I think that someone with self-view might have an experience and say, "this is self" -- note that in this way, as a result of this, the self-view is self-perpetuating.

Conversely, without self-view you might have an experience (a thought, a feeling) and observe that "that was some conceit".

The ten fetters have the eradication of the identity-view or belief in a self (sakkāya-diṭṭhi) as a lower fetter, that has to be done in order to become a sotapanna or stream winner.

It's actually the other way around, meaning becoming a stream enterer will be 'done' before the belief in a self is eradicated.

After becoming a stream enterer you'll realise that you are nothing more than a process (for the lack of words). Before becoming a stream enterer the mind will pick and observe one of the three characteristics: anicca, dukkha or anatta. And when this characteristic is understood/seen completely the mind will release and let go.

And even though the stream winner knows then, from experience, that (s)he is nothing more than a process it doesn't mean that (s)he also experience everything impersonal. Awareness itself for instance will still feel as 'I am aware of this or that'. The difference is between deeply knowing from experience (entering the stream) and experiencing or feeling, or sense of self as you put it.

That sense of self will be eradicated with the uprooting of conceit.